many-worlds hypothesis

Disclaimer. I am not a physicist. Please step in, write a better writeup, and /msg me to have this clumsy attempt nuked out of orbit. Thanks.

At the quantum level, objects (elementary particles) are so tiny, they can no longer be said to have a definite position, velocity, mass, and energy; the world is described more accurately, at this level, in terms of wave functions that correlate these entities. These functions can be interpreted as describing the probability of an elementary particle having a particular position, velocity, mass, energy at a particular time.

So think of the world at the quantum level as being described by a gigantic system of equations, each representing the continuum of possible states of a single elementary particle. The effect of a measurement, the observation of a particle, is to fill in some of the values in this equation, which effectively results in a new system of equations. The first system of equations predicted the exact outcome of the measurement, in the sense that it predicted a continuum of possible outcomes ("possible realities"), with the relative probability for each of these to occur. The actual observation has 'proved' one of these possibilities to be reality. Mathematically, it simplifies the system of equations; those equations now describe all possible outcomes of any further possible measurements consistent with the measurement that just took place (and all the measurements before it, if any).

So we can think of any such system as representing a mindblowing number of possible combinations of position, velocity, mass, and energy of elementary particles. Any such combination can be thought of as a 'possible world'; if all possible measurements could actually be done, one of them would emerge as the actual world we live in.

This description is known as the many worlds interpretation of quantum physics. It is an attempt to formulate in natural language what is really a mathematical property of the mathematical constructs used to describe the world at the level of elementary particles.

Such interpretation has no meaning in physics. The substance of quantum physics is formed by mathematical models that relate the probabilities of the outcomes of measurements; their validity is assessed by checking if actual measurements in the real world correspond to the predictions made by the model. The business of physics is to propose, refine and verify such models, in order to provide more and more accurate predictions of the measurements made in reality. Calling a particular mathematical construct within the model a world, or a possible world, takes the discussion outside the realm of science, and into metaphysics, which, to scientists, can be described as the study of how we conceive of the world. Put another way, it is a study of what we mean exactly when we use the words 'possible' and 'world'.

The two-slit experiment, the simplest demonstration of irreducibly quantum phenomena, shows that there are things that behave like photons in every way -- interception, reflection, path, interference -- and which are totally undetectable except by the interference they cause with the kind of photons we can detect.

This is not the place to go into the slit experiment in detail. Anyway, I want you to read the book. The Fabric of Reality is one of the most important popular scientific books of the age. I thought the whole idea was nonsense before I tackled Deutsch -- but my philosophical training was wrong.

However, the point is: the two-slit experiment shows that real photons behave as if there exist other entities that are exactly like photons, undetectable except for their interaction with real photons. You can call them "shadow" photons, you can go back to mediaeval scholastic terminology and call them photons in posse. Unnecessary semantic quibbles. You can bury your head in the sand, the way the traditional Copenhagen interpretation does.

The simplest explanation is that they're photons.

The simplest explanation for the quantum slit experiment and for all of quantum physics, the most rock-bottom certain theory that has ever been devised, is that there is another shadow universe of photons out there, interacting with the one we can detect.

And when you do the calculations in detail, it's not just one shadow universe, it's not just photons, it's all quantum events. All possible quantum events really happen.

It is the ultimate Copernicandethronement. There is no one "me" in one infinitesimal slice of possibility; all the events possible in the quantum underworld are real, and all the bifurcations in reality they cause. It is not, pacerp, a formalism in equations waiting for observation. It is simpler -- it is a better explanation -- to say that this is all real. There are no good grounds for holding that some possibilities are real and others aren't. There is no privileged reality, no unique observer.

This explanation of why we see the quantum observations we do, is a better theory: it stands up to the alternatives in a critical, evolutionary way. There seem to be two serious alternatives: one of repeated evolution of a bounded cosmos through time or hyper-time (espoused by Lee Smolin in The Life of the Cosmos), and the old search for mathematical constraints that make our present anthropic universe logically necessary.

Neither of these others thoroughly explains what we see. The quantum many-worlds theory does.

Imagine if you will, the universe starting in the big bang, much like a bottle of perfume being un-stoppered in a room, and the molecules of scent diffusing throughout the space. Okay, now imagine that each molecule represents one precise arrangement of matter and energy of the entire universe (or its quantumwavefunction, if you prefer). The position in this room is equivalent to a coordinate in phase space (follow dat link) that the universe occupies. Coordinates that are close together in phase space might represent universes that are nearly the same..

As the universe evolves over time, it moves from position to position in phase space, and the likelihood of it going from any one position to another can be determined by quantum mechanics. In the many world picture of things, all possiblities open to the universe, at anyone time exist; or all the molecules of perfume really are there. With the Copenhagen interpretation they may or may not exist, but one definitely does when an observation is made, and all the others do not!

In the many worlds universe, what we experience is in fact a path being drawn from coordinate to coordinate through the total phase space of the universe, back through time until the start of the universe, position zero. I imagine it as a chain of perfume molecules linked together, leading back into the perfume bottle.
This theory is said to be untestable, as the different universes aren't supposed to be able to effect each other. Some people say that aspects of paranormal experiences can be explained if the theory is true however; perhaps ghosts etc. are events in a universe near to ours in phase space quantum tunneling through to our own.

It might be that if any of this 'universe to universe' interaction goes on, it has a low probability of happening, and any particle physics experiments set up to test it may have an infinitesimal chance of working. However, on a universal scale the effects will most likely be cumulative, perhaps affecting cosmology. Incidently recent measurements of supernova have shown the universe may well be expanding at an ever increasing rate, for reasons that are as yet, unprovable!

One of the principal misconceptions about the many-worlds theory is that it involves the creation of new worlds. It does not. What it does involve is the partition of the world's wavefunction into distinct cases that might as well be different worlds. This partitioning is not a new mechanism -- it is needed to explain many testable quantum phenomena, such as the two-slit experiment. What is different is the recognition that this mechanism is adequate to explain our observations on its own, without the need for any additional rules to be added.

Let's look at a system: a two-slit diffraction experiment. We have an electron shot at a barrier with two slits in it. We can choose to measure at the barrier whether the electron passes through each slit, or we can choose not to measure this. We can also measure the position at which the electron hits a target on the far side of the barrier. The system is supposed to be very 'clean' with the particles not losing coherence quickly, even when passing through the detectors (this is hard to do, but it can be done).

As we start out, there are three basic divisions in the components of the electron's wavefunction:

If we choose to measure only at the target, then the three components add together, interfering. Options A and B add up to a two-slit pattern on the target; option C does not contribute to wavefunction at the target because it was blocked at the barrier (but it does add some intensity on the other side of the barrier, where the electron would go undetected).

According to Many Worlds, the detector's wavefunction splits up into independent components just like the electron's did just a moment ago. This time there are many more components, and the detector is bigger than an electron, but that is irrelevant -- it is still the same mechanism.

What happens if we choose to measure at the barrier and the target?

According to the Copenhagen interpretation, our detector at the barrier forces the universe to pick option A, B, or C, destroying the other components, then our second detector forces the universe to pick again, for the final position of the electron -- since it has already forced it out of all but one component, it will use the one that survived the last round of measurement.

According to Many Worlds, our detectors all become quantum-entangled with the electron, which proceeds just as before. With the detectors entangled, the various outcomes proceed independently of each other. However, by having our detection in two tiers, we pre-partition ourselves into the A component and B component (and C component), which prevents interference at the later stage.

So, let's compare the two pairs of results. In particular, the fate of the electron.

In the Copenhagen interpretation, the electron's fate is intimately tied to the on/off switch on a detector which exerts the same force on the electron whether it is on or off (or, if there is a difference, the change in outcome is completely incommensurate to the change in strength of that force).

In the Many-Worlds theory, the electron is not affected by the on/off setting of the detector. It is the detector which is affected by its own on/off setting.

You decide which makes more sense.

Many Worlds also has the virtue of maintaining locality in the face of the Einstein-Podolsky-Rosen paradox. The instantaneous information transfer is only required when the second wavefunction collapses. However, in many-worlds, wavefunctions do not collapse. Thus, there is no need for instantaneous information transfer at all.

But how, then, do we not observe kooky quantum effects in the macro world, if there's no special rule to keep them out? Well, what kooky quantum effects are we missing?

Heisenberg Uncertainty: have YOU ever simultaneously measured your position and momentum (or any other appropriate pair of properties) to precision better than Planck's constant? I didn't think so. The restriction here is so remote that we don't notice it.

Tunnelling across classically prohibited barriers: probability of tunnelling decays exponentially with width and strength of barrier. Any barrier big enough for us to notice is far far too big to tunnel across.

Wavefunction interference: this may happen all the time everywhere, but it's hard to notice except with multiple measurements on systems which are identical to the point of coherence. The complexity of macroscopic objects makes it impossible to achieve even approximate identicality, and even if we could get the atoms into the right places, they wouldn't be coherent (the difficulties in achieving this are known, unsurprisingly, as decoherence).

Objects being spread out over distances: It's only before you look at it that its location is undetermined to you. Did your wallet spread out over time while you weren't looking? Well, assuming there was a possibility that some force would come along and displace it, yes, it is spread out. However, the moment you find it, you find it all in one place (unless the force was one that would destroy the wallet). Why? The moment you have enough information to confirm one outcome of the wallet for yourself, you are entangled with that one and you cannot observe the effects of the others. If you do try to perform interference experiments to tease this diffusion out of the system, you will run into the decoherence problems noted above, for Wavefunction Interference.

One critique of Many-Worlds is that one loses justification for the Born Probabilities. This is a bit rich since the Copenhagen Interpretation includes them as a separate axiom. But more to the point, all you need to get out the Born Probabilities is the notion that the wavefunction can be interpreted such that some set of mutually orthogonal subspaces represent probabilities. The Born Probabilities immediately result from the Pythagorean Theorem. All the difficulty is apparently in connecting 'this is real' to 'you can treat it as if it was what reality is made of, in the way that it looks like it actually does', which I find somewhat baffling.

It has been pointed out that a detector does not need to be on in order to 'measure' the system as far as the Copenhagen Interpretation is concerned. This is only going to be true if the detector is disordered enough to cause decoherence. If the detectors are adequately quiet, inactive detectors do not need to cause decoherence (and even if they are on, if they are designed properly). I have only considered this quiet case above.

Secondly, since there are many partitions, but only one greater universe, I prefer a different name-root than 'Many Worlds', perhaps 'Universal Entanglement' or 'Non-Collapsing Wavefunction'. However, we seem to be pretty solidly stuck with 'Many Worlds' as the recognized name for this idea.